The Electromagnetic Ocean

NODE 01

The Great Unification

EB

• Changing E-field → B-field. Changing B-field → E-field.
• Self-propagating disturbance.
• Electricity + Magnetism = Electromagnetism.

NODE 02

Maxwell's Vision

∇·E=ρ/ε₀

∇·B=0

∇×E=-∂B

∇×B=μJ+με∂E

• Gauss (E), Gauss (B), Faraday, Ampère-Maxwell.
• Understand physical meaning, not just math.

NODE 03

Displacement Current

∂E/∂t→B

• Maxwell added changing E-field to Ampère's law.
• Completes symmetry for EM wave propagation.

NODE 04

EM Wave

• Oscillating E and B fields propagate through space.
• E ⊥ B ⊥ direction of propagation.
• Transverse wave.

NODE 05

Field Orientation

• E and B oscillate together.
• Fixed phase relationship in vacuum (ideal plane wave).

NODE 06

Speed of EM Waves

c

• c = 1/√(μ₀ε₀).
• In vacuum: c ≈ 3.00 × 10⁸ m/s.
• Connects EM theory to observed speed of light.

NODE 07

Light is EM

• Visible light IS electromagnetic radiation.
• Radio, X-rays, etc. are not separate types of wave.
• Occupy diff regions of same spectrum.

NODE 08

Freq & Wavelength

HIGH fSHORT λ

LOW fLONG λ

• Universal wave relation in vacuum: c = fλ.
• Higher freq → shorter wavelength.

NODE 09

Energy of EM Rad

• Quantum preview: E = hf.
• Bridge: Classical wave (f, λ) → Quantum (photon energy).

NODE 10

EM Spectrum

RADIOGAMMA

• Radio → Micro → IR → Visible → UV → X-Ray → Gamma.
• Boundaries are conventional, not absolute walls.

NODE 11

Radio Waves

• Long λ, low f.
• Broadcasting, communication, navigation, astronomy.

NODE 12

Microwaves

• Radar, satellite comms, heating, remote sensing.
• Shorter λ than radio.

NODE 13

Infrared (IR)

• Beyond red end of visible.
• Thermal imaging, remote controls, heating.
• Connects to Realm 10 (thermal radiation).

NODE 14

Visible Light

• Detected by human visual system.
• Approx: 400 - 700 nm.

NODE 15

Colour & Wavelength

• Spectral colours correspond to wavelengths.
• Red = longer λ. Violet = shorter λ.

NODE 16

Ultraviolet (UV)

• Higher f than visible violet.
• Sterilization, fluorescence, astronomy.
• UV-A, UV-B, UV-C.

NODE 17

X-Rays

• High-energy, penetrating, ionizing.
• Medical imaging, crystallography.
• Generated by accelerated electrons hitting targets.

NODE 18

Gamma Rays

• Very high f. Nuclear transitions, radioactive processes.
• Medical treatment, nuclear science.

NODE 19

Spectrum Comp

RADIOLONG λ

VISIBLEMID λ

GAMMASHORT λ

• Visual table comparison.
• Region boundaries are not infinitely sharp.

NODE 20

Polarization

• E-field orientation. Possible because EM waves are transverse.
• Unpolarized, Plane polarization, Polarizer.

NODE 21

Linear Polarization

• E-field oscillates in one preferred transverse direction.
• Polarization axis, transmission axis.

NODE 22

Malus's Law

I=I₀ cos²θ

• Ideal polarized light passing through analyzer.
• Analyzer angle, transmitted intensity.

NODE 23

Unpolarized Light

• E-field orientation is random over many cycles.
• After ideal linear polarizer: I = I₀/2.

NODE 24

Brewster's Angle

• Polarization by reflection.
• tan θB = n₂/n₁.
• Reflected wave has strong polarization. Bridge to optics.

NODE 25

EM in Matter

v≈c/n(v = fλ)

• Prop speed differs from vacuum.
• Simple non-magnetic dielectric: v ≈ c/n.

NODE 26

Refractive Index (n)

n=c/v

• n = c/v. Vacuum speed / Medium speed.
• Optical density as an informal concept.

NODE 27

Freq vs Wavelength

f = CONST(SOURCE)

v, λ CHANGE(MEDIUM)

• During refraction (stationary boundary):
• Freq remains continuous. Speed changes → λ changes.

NODE 28

Rad Pressure

• EM radiation carries momentum.
• Can exert pressure. Solar sails, optical forces.

NODE 29

Intensity

• I = power/area.
• Isotropic source in free space: I ∝ 1/r².

NODE 30

EM Energy Density

u_E =½ε₀E²

u_B =B²/(2μ₀)

• In vacuum, E and B contributions are equal in magnitude on average for ideal plane wave.

NODE 31

Poynting Vector

S=E×B

• Direction and rate of EM energy flow.
• Magnitude = energy flow per unit area per time.

NODE 32

EM Momentum

p=E/c

• Radiation carries momentum (p = E/c).
• Not merely "light energy", has momentum effects.

NODE 33

Emit & Absorb

• Matter emits, absorbs, scatters EM radiation.
• Diff wavelengths interact differently. (Spectroscopy).

NODE 34

Scattering

• Rayleigh, Mie, Atmospheric scattering.
• Blue sky, red sunsets, clouds.

NODE 35

Atmos EM

• Solar rad, visible, UV, IR.
• Ozone UV filtering, Greenhouse absorption.

NODE 36

Radio Comm

• Info → Modulation → EM Carrier → Transmit → Receive → Demod.

NODE 37

Radar

• Transmit EM wave → interact with target → receive return.
• Infer distance/motion (Time delay, Doppler).

NODE 38

Satellite Comm

• EM waves for long distance.
• Freq bands, Line of sight, Satellite relay.

NODE 39

Fibre Optics Pre

• Light guided by repeated internal reflection.
• Core, cladding. Detailed optics in Realm 23.

NODE 40

EM in Medicine

RFIRUVXγ

• RF (comms), IR (thermal), Visible (imaging), UV (steril).
• X-rays (imaging), Gamma (radiotherapy).

NODE 41

Astro Windows

• Diff environments emit diff wavelengths.
• Radio, IR, Optical, UV, X-ray, Gamma astronomy.
• Visible universe is only one slice.

NODE 42

Spectroscopy

• Matter produces characteristic EM spectra.
• Emission/Absorption, Spectral lines. Bridge to Realm 26.

NODE 43

EM Generation

• Accelerating charges radiate EM energy.
• Oscillating charges generate radiation across many freqs.

NODE 44

Antennas

• Converts electrical oscillations into EM radiation.
• Resonant dimensions, radiation pattern, polarization.

NODE 45

EM Propagation

VACUUMMATTERREFLECTDIFFRACT

• Reflect, Refract, Diffract, Interfere, Scatter.
• Prepares transition to Optics realms.

NODE 46

Relativity Preview

c=CONSTANT

• Constancy of light speed in inertial frames.
• Foundation of special relativity (Realm 30).

NODE 47

Experiment Lab

POL

SPEC

REFL

DIFF

• Polarization (Malus), Spectrum (Spectroscope).
• Reflection, Diffraction, Microwave interference.

NODE 48

Graph Chamber

• Freq vs Wavelength, Malus (I vs θ).
• Rad intensity (I vs 1/r²), Refractive index (n=c/v).

NODE 49

Misconceptions

X

• "EM needs air" → No, propagates in vacuum.
• "Only visible is EM" → Visible is a tiny slice.
• "E parallel to B" → No, perpendicular.

NODE 50

Solving Engine

• ID Region → Find f or λ → c=fλ (v=c/n).
• Field problem? E, B, Maxwell.
• Polarization? Malus. Energy? I=P/A.

NODE 51

Master Map

ΔE ↔ ΔBEM WAVE → LIGHTRADIO ... GAMMA

• The entire realm compressed.

NODE 52

Deep Synthesis

R15-R20 (WIRES)↓R21 (SPACE)

• R15-R20 built the EM machinery in wires.
• R21: The disturbance leaves the circuit and travels space.
• This is one of the most beautiful chains in Physics.